The path-coalescence transition and its applications

Abstract

We analyse the motion of a system of particles subjected a random force fluctuating in both space and time, and experiencing viscous damping. When the damping exceeds a certain threshold, the system undergoes a phase transition: the particle trajectories coalesce. We analyse this transition by mapping it to a Kramers problem which we solve exactly. In the limit of weak random force we characterise the dynamics by computing the rate at which caustics are crossed, and the statistics of the particle density in the coalescing phase. Last but not least we describe possible realisations of the effect, ranging from trajectories of raindrops on glass surfaces to animal migration patterns.

4 pages, 3 figures; revised version, as published

References in corpus (3)

• Coherent Branched Flow in a Two-Dimensional Electron Gas
• Statistics of branched flow in a weak correlated random potential
• Statistics of finite-time Lyapunov exponents in a random time-dependent potential

Cited by in corpus (62)

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• Caustic activation of rain showers
• Statistical models for spatial patterns of heavy particles in turbulence
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• Fluctuation Relations for Diffusion Processes
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• Fluctuation relations in simple examples of non-equilibrium steady states
• Distribution of relative velocities in turbulent aerosols
• Clustering of particles falling in a turbulent flow
• Clustering in mixing flows
• Lagrangian tracers on a surface flow: the role of time correlations
• Inertial-particle dynamics in turbulent flows: caustics, concentration fluctuations, and random uncorrelated motion
• Unmixing in Random Flows
• Relative velocities of inertial particles in turbulent aerosols
• Stochastic suspensions of heavy particles
• Anomalous diffusion in random dynamical systems
• Generalised Ornstein-Uhlenbeck processes
• On the Aggregation of Inertial Particles in Random Flows
• Strong clustering of non-interacting, passive sliders driven by a Kardar-Parisi-Zhang surface
• Large compact clusters and fast dynamics in coupled nonequilibrium systems
• Localization-delocalization transitions in turbophoresis of inertial particles
• Distribution of velocity gradients and rate of caustic formation in turbulent aerosols at finite Kubo numbers
• Crystallization and melting of bacteria colonies and Brownian Bugs
• Inertial particles driven by a telegraph noise
• Replica symmetry breaking in trajectories of a driven Brownian particle
• Relative velocities in bidisperse turbulent suspensions
• Active turbulence and spontaneous phase separation in inhomogeneous extensile active gels
• Eddy diffusivities of inertial particles under gravity
• Ergodic properties of a model for turbulent dispersion of inertial particles
• Perturbation theory for a stochastic process with Ornstein-Uhlenbeck noise
• Clustering, intermittency and scaling for passive particles on fluctuating surfaces
• Statistical model for collisions and recollisions of inertial particles in mixing flows
• Caustics in turbulent aerosols form along the Vieillefosse line at weak particle inertia
• Collisions of particles advected in random flows
• Lyapunov exponents for particles advected in compressible random velocity fields at small and large Kubo numbers
• Rate of formation of caustics in heavy particles advected by turbulence
• Stochastic processes in turbulent transport
• Fractal catastrophes
• Aggregation and fragmentation dynamics in random flows: From tracers to inertial aggregates
• Time evolution of intermittency in the passive slider problem
• Convergent Chaos
• Dynamics of path aggregation in the presence of turnover
• Diffusion, super-diffusion and coalescence from single step
• Concentration fluctuations of large Stokes number particles in a one-dimensional random velocity field
• Multiple regimes of diffusion
• Localization-delocalization transition for light particles in turbulence
• Heavy particles in a persistent random flow with traps
• Phase transitions in the distribution of inelastically colliding inertial particles
• Lacunarity Exponents
• Clustering and collision of inertial particles in random velocity fields
• Perturbation theory for large Stokes number particles in random velocity fields
• Renormalized transport of inertial particles in surface flows
• Eddy diffusivity of quasi-neutrally-buoyant inertial particles
• Solution of the Stochastic Langevin Equations for Clustering of Particles in Turbulent Flows in Terms of Wiener Path Integral
• Settling velocity of quasi-neutrally-buoyant inertial particles
• Fractal dimensions and trajectory crossings in correlated random walks
• Lyapunov exponent for small particles in smooth one-dimensional flows
• Point-source inertial particle dispersion
• A lattice model for the Eulerian description of heavy particle suspensions
• Point-source dispersion of quasi-neutrally-buoyant inertial particles
• Numerical Coalescence of Chaotic Trajectories
• Dynamics of inertial particles in a random flow with strong permanent shear